I wasn't sure if a Child Flex Card can launch another child flex card as flyout action. I tried and apparently it is possible.
First create a regular flex card, lets name it P1. And then create two separate Child Flex Card, C1 and C2.
Under the Action of C1, launch flyout C2. Under the Action of P1, launch flyout C1.
The result would look like this

Salesforce recommends certain measures while implementing multiple level flyouts so please check this article before you implement.
https://help.salesforce.com/s/articleView?id=xcloud.os_embed_flexcard_inside_another_flexcard.htm&type=5